Higher-order Time Integration Schemes for Aeroelastic Applications on Unstructured Meshes

Efficient techniques for computational aeroelasticity (CA) on unstructured meshes are investigated. These include the formulation of a fourth-order implicit Runge-Kutta timeintegration scheme (IRK64) and a third-order backwards difference time-integration scheme (BDF3) as well as a second-order backwards difference time-integration scheme (BDF2) for the coupled system of flow and structural equations. Strong coupling between the flow solution and structural equations is maintained by fully converging the fully coupled system at each time step or stage. The time integration schemes are constructed such that discrete conservation is maintained in the flow solution in the presence of dynamically deforming meshes by verifying the Discrete Geometric Conservation (DGCL) law. Efficient multigrid solution techniques are devised for solving both the governing flow equations, and the mesh motion equations, using the same agglomerated coarse levels for both problems. The flutter boundary prediction of the AGARD 445.6 wing is used to demonstrate the accuracy and efficiency of these techniques as well as the sensitivity of flutter boundary prediction to time step size and temporal errors.